I replaced the driver side rear sway bar link on my 97 Sable over the
weekend. I have no idea how long it may have been broke. There was
a small popping noise for quite a while. That popping noise became more
distinct and louder a week back.

Question:
What problems make have been caused by the broken sway bar link?

Lance,
Not sure what could have been done, but I had the same happen to me but on the passenger side. I replaced both sides with the Heavy Duty links (they were like 5/8" diameter). The mounting stud rusted off the bottom of the old link. I have not noticed any additional problems as a result of this happening. The only thing I can think of is maybe the alignment. I plan on replacing my struts/springs on the rear before I have the alignment done anyway, which will be real soon.